 5.5 Call \(\mathsf {LLD_{sp}}\)  the full subcategory of \(\mathsf {MSN_{sp}}\)  that
consists of lld MSNs, and consider the forgetful functor
\(\mathsf {Forget} \colon \mathsf {LLD_{sp}} \rightarrow \mathsf {MSN_{sp}}\) . In
categorical terms, an lld version is the coreflection of an MSN \((X,{A}, {N})\)  along the functor \(\mathsf {Forget}\) , see
[1]}. In this paper, we do not answer the question whether there exists an lld version for
each saturated MSN. This is equivalent
to the existence of a right adjoint \(\mathsf {R}\)  of
\(\mathsf {Forget}\) . As a matter of fact, if such an adjoint exists,
there would be a natural transformation \(\varepsilon \colon \mathsf {Forget} \circ \mathsf {R} \Rightarrow \operatorname{\mathrm {id}}_{\mathsf {MSN_{sp}}}\)  such
that the pair \([\mathsf {R}(X, {A}, {N}), \varepsilon _{(X, {A},{N})}]\)  gives the lld version of any saturated MSN \((X, {A},{N})\) .
